Iraqi Kurds take part in a demonstration outside the US consulate in Erbil, the capital of autonomous Iraqi Kurdistan, on October 21, 2017, to protest against the escalating crisis with Baghdad. SAFIN HAMED/AFP

The Kurdistan Regional Government (KRG) offered on Wednesday to put an independence referendum on hold as part of efforts to end the military confrontation with Iraqi forces, and resolve the crisis with the central government in Baghdad through dialogue.

But a Iraqi military spokesman suggested an offensive to wrest back Kurdish-held territory would continue regardless.

The Iraqi government has transformed the balance of power in the north of the country since launching a campaign last week against the Kurds, who govern an autonomous region of three northern provinces.

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The KRG proposed an immediate ceasefire, a freezing of the results of a September referendum in which Kurds voted overwhelmingly for independence, and "starting an open dialogue with the federal government based on the Iraqi Constitution."

The Iraqi government has transformed the balance of power in the north of the country since launching a campaign last week to seize back territory from the Kurds, who govern an autonomous region of three northern provinces and had also seized a swathe of other territory in northern Iraq.

In a brief social media comment hinting that the campaign would continue, an Iraqi military spokesman said: "Military operations are not connected to politics."

Prime Minister Haidar Abadi has ordered his army to recapture all disputed territory and has also demanded central control of Iraq's border crossings with Turkey, all of which are inside the Kurdish autonomous region.

Kurdish Peshmerga forces beat back an advance by Iranian-backed pro-government paramilitaries on Tuesday in the region of Rabi'a, 40 kilometers (25 miles) south of the Fish-Khabur border area with Turkey and Syria, Kurdish officials said.

Fish-Khabur is strategically vital because oil from both Kurdish and government-held parts of northern Iraq cross at a pipeline there into Turkey, the main route out of the area for international export, crucial for any Kurdish independence bid.

The fighting so far has taken place outside the Kurdish autonomous region, but Fish-Khabur is located within it.

The fighting between the central government and the Kurds is particularly tricky for the United States which is a close ally of both sides, arming and training both the Kurds and the central government's army to fight against Islamic State.

The Iraqi government's advance over the past week has been achieved with comparatively little violence, with Kurds mostly withdrawing without a fight.

He had yet to react to the Kurdish proposal on Wednesday, when he began an official visit to neighbouring Turkey and Iran during which relations with the Kurds -- whose communities are established in parts of all three countries as well as Syria -- will be high on the agenda.

Iran announced the reopening of one of the border crossings with the Kurdistan region of Iraq, closed last week in support of the Iraqi government.

Strategically vital

Abadi, who has the backing of Tehran and Ankara to act against the KRG, has ordered his army to recapture all disputed territory and has also demanded central control of Iraq's border crossings with Turkey, all of which are inside the Kurdish autonomous region.

Kurdish Peshmerga forces beat back an advance by Iranian-backed pro-government paramilitaries on Tuesday in the region of Rabi'a, 40 kilometers (25 miles) south of the Fish-Khabur border area with Turkey and Syria, Kurdish officials said.

Fish-Khabur is strategically vital because oil from both Kurdish and government-held parts of northern Iraq crosses at a pipeline there into Turkey, the main route out of the area for the international exports that are crucial to any Kurdish independence bid.

The fighting so far has taken place outside the Kurdish autonomous region, but Fish-Khabur is inside it.

The fighting between the central government and the Kurds is particularly tricky for the United States which is a close ally of both sides, arming and training both the Kurds and the central government's army to fight against Islamic State.

The Iraqi government's advance over the past week has been achieved with comparatively little violence, with Kurds mostly withdrawing without a fight.

Iraqi forces are preparing in parallel an offensive to recapture the last patch of Iraqi territory still in the hands of Islamic State, on the border with Syria, the military said on Wednesday.

The militant group also holds parts of the Syrian side of the border, but the area under their control is also shrinking there as they retreat in the face of two sets of hostile forces - a U.S.-backed, Kurdish-led coalition and Syrian government troops with foreign Shi'ite militias backed by Iran and Russia.

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